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An Hélein's type convergence theorem for conformal immersions from $ \mathbb{S}^{2}$ to manifold


Author: Guodong Wei
Journal: Proc. Amer. Math. Soc. 147 (2019), 4969-4977
MSC (2010): Primary 53C42; Secondary 53A30, 53A07
DOI: https://doi.org/10.1090/proc/14614
Published electronically: June 10, 2019
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Abstract: In this short paper, we establish an Hélein's type convergence theorem for conformal immersions from $ \S ^{2}$ to a general compact Riemannian manifold. As an application, we extend the existence of minimizer of $ \int \vert A\vert^{2} d\mu $ for immersed 2-spheres in compact 3-manifolds under certain conditions due to E. Kuwert, A. Mondino, and J. Schygulla to higher codimensions.


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Additional Information

Guodong Wei
Affiliation: Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China
Email: weiguodong@math.pku.edu.cn

DOI: https://doi.org/10.1090/proc/14614
Received by editor(s): November 19, 2018
Received by editor(s) in revised form: February 24, 2019
Published electronically: June 10, 2019
Additional Notes: This work was supported by National Natural Science Foundation of China (Grants No. 11671015 and 11731001).
Communicated by: Guofang Wei
Article copyright: © Copyright 2019 American Mathematical Society